For another exposition of the same (or similar) results, see also Dan Piponi's post from 2008 "What does topology have to do with computability?" at http://blog.sigfpe.com/2008/01/what-does-topology-have-to-do...
Also, as a follow-up, you may be interested in Martin Escardo's 2007 post on the same blog: http://math.andrej.com/2007/09/28/seemingly-impossible-funct...
For another exposition of the same (or similar) results, see also Dan Piponi's post from 2008 "What does topology have to do with computability?" at http://blog.sigfpe.com/2008/01/what-does-topology-have-to-do...
Also, as a follow-up, you may be interested in Martin Escardo's 2007 post on the same blog: http://math.andrej.com/2007/09/28/seemingly-impossible-funct...